Invited Lecture
Numerical long-time conservation of energy, momentum and actions for nonlinear wave equations
University of Geneva, Switzerland
Abstract
This talk considers nonlinearly perturbed wave equations,
pseudo-spectral semi-discretizations and full discretizations
using trigonometric time integrators. The long-time
near-conservation of energy, momentum, and harmonic actions
is studied. Rigorous statements are shown under suitable
numerical non-resonance conditions and under a CFL condition.
The time step is not assumed to be small compared to the
inverse of the largest frequency in the space-discretized system,
so that classical backward error analysis cannot be applied.
The proofs of the statements on the long-time conservation
properties are based on the technique of modulated Fourier
expansions.
This is joint work with Christian Lubich and David Cohen. Related publications (2008) can be downloaded from http://www.unige.ch/~hairer/preprints.html
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